*4.1. Obtaining Information Time*

The most correct method of determinization of obtaining information time of failures in electrical networks (*t*obt.infor) is the Delphi method. This method was successfully applied in different researches, e.g., [35,36].

The questionnaire was prepared specifically for this research. It was given to twenty experts working in PS companies (dispatchers). The experts had at least five years employment experience.

This research proposes obtaining information time in 12 intervals. The specialists had to give a score from one to ten for each time interval. The most probable time interval got ten points from experts while the least probable got zero points. In the case that the expert indicates the same time interval probability, they could estimate the time intervals by points. The harmonization degree of the participant of the questionnaire was calculated. For this, a concordance coefficient (Equation (6)) proposed by Kendall was used:

$$\begin{array}{l} \text{W} = \frac{12 \times \text{S}}{\text{m}^2 \times (\text{m}^3 - \text{n})},\\ \text{W} = \frac{12 \times 35.9 \times 10^3}{20^2 \times (12^3 - 12)} = 0.62 \end{array} \tag{6}$$

where


$$W = \frac{12 \times 35.9 \times 10^3}{20^2 \times (12^3 - 12)} = 0.62\tag{7}$$

The arithmetic mean of all estimates was determined in accordance with the well-known Equation (8):

$$\overline{N} = \frac{\sum\_{i=1}^{n} \sum\_{j=1}^{n} N\_{ij}}{\frac{12}{12} + 180 + 164 + 135 + 117 + 97 + 71 + 61 + 57 + 41 + 31 + 19}} = 95.4 \tag{8}$$

The sum of the squares of differences was determined according to Equation (9):

$$S = \sum\_{i=1}^{n} \left( \sum\_{j=1}^{m} N\_{ij} - \overline{N} \right)^2 \tag{9}$$

$$S = (5.8 + 7.1 + 4.7 + 1.5 + 0.5 + 0.00256 + 0.6 + 1.2 + 1.5 + 3 + 4.2 + 5.8) \times 10^3 = 35.9 \times 10^3 \tag{9}$$

Since the time intervals were indicated in the questionnaires, fixed points were chosen for calculating the expectation at each interval. These points corresponded to the middle of the intervals. The mathematical expectation was determined by the following equation:

$$M(t) = \frac{\sum\_{i=1}^{n} (t\_{ci} \sum\_{j=1}^{m} N\_{ij})}{\sum\_{i=1}^{n} \sum\_{j=1}^{m} N\_{ij}} \tag{10}$$
  $M(t) = \frac{21.5 + 67.5 + 102.5 + 111.3 + 131.6 + 133.3 + 115.3 + 114.3 + 121.1 + 97.3 + 81.0 + 54.0}{1145} = 1.01$ 

where


The calculation results are indicated in Table 1.

For clarity, the distribution of expert estimates given to the corresponding time interval is presented in Figure 2.

**Figure 2.** The histogram that represents the assessment of experts concerning a distribution of the time for obtaining information on failures.

The mathematical expectation of obtaining information time on failures was 1.01 h with the concordance coefficient of 0.627. In the questionnaires, it was considered that there were no monitoring systems of electric network, i.e., a PS company dispatcher obtained information on failures from the consumers.

This is quite a long time, which can and should be reduced by various means. A proposition to reduce the time may be, e.g., an automatic detection of failures facts and places in electrical networks and unmanned aerial vehicles allowing to monitor the power line state and detect failure places.

**Table 1.** The results of the expert survey to determine the time for obtaining information on failures.

